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摘要翻译：
有限混合模型在应用计量经济学中是有用的。它们可以用来对未观测到的异质性进行建模，在劳动经济学、产业组织等领域发挥着重要作用。混合物在处理污染采样模型和多重平衡模型时也很方便。本文证明了有限混合模型在弱假设下的非参数辨识，这些假设在经济应用中是合理的。关键是利用协变量变异中信息所隐含的识别能力。首先，在不同的非嵌套充分条件集下，给出了三种识别方法。数据的可观察特征告诉我们这三种方法中哪一种是有效的。这些结果适用于一般的非参数转换回归，也适用于结构计量经济模型，如具有未观察到的异质性的拍卖模型。其次，对辨识结果进行了一些扩展。特别地，其中混合权重以完全不受限制的方式依赖于回归器的值的混合回归被示出是非参数可识别的。这意味着一个具有函数值未观察到的异质性的有限混合模型可以在一个横截面环境中被识别，而不限制回归子与未观察到的异质性之间的依赖模式。在这方面，它类似于固定效应面板数据模型，允许未观察到的异质性和协变量之间不受限制的相关。第三，本文通过形成一种新的辨识策略的样本模拟，证明了对整个混合模型的完全非参数估计是可能的。与标准非参数估计问题一样，尽管模型具有非正则性，估计量仍具有理想的多项式收敛速度。
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英文标题：
《Nonparametric Analysis of Finite Mixtures》
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作者：
Yuichi Kitamura, Louise Laage
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最新提交年份：
2018
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分类信息：
一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
Finite mixture models are useful in applied econometrics. They can be used to model unobserved heterogeneity, which plays major roles in labor economics, industrial organization and other fields. Mixtures are also convenient in dealing with contaminated sampling models and models with multiple equilibria. This paper shows that finite mixture models are nonparametrically identified under weak assumptions that are plausible in economic applications. The key is to utilize the identification power implied by information in covariates variation. First, three identification approaches are presented, under distinct and non-nested sets of sufficient conditions. Observable features of data inform us which of the three approaches is valid. These results apply to general nonparametric switching regressions, as well as to structural econometric models, such as auction models with unobserved heterogeneity. Second, some extensions of the identification results are developed. In particular, a mixture regression where the mixing weights depend on the value of the regressors in a fully unrestricted manner is shown to be nonparametrically identifiable. This means a finite mixture model with function-valued unobserved heterogeneity can be identified in a cross-section setting, without restricting the dependence pattern between the regressor and the unobserved heterogeneity. In this aspect it is akin to fixed effects panel data models which permit unrestricted correlation between unobserved heterogeneity and covariates. Third, the paper shows that fully nonparametric estimation of the entire mixture model is possible, by forming a sample analogue of one of the new identification strategies. The estimator is shown to possess a desirable polynomial rate of convergence as in a standard nonparametric estimation problem, despite nonregular features of the model.
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PDF链接：
https://arxiv.org/pdf/1811.02727
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